AbstractWe extend epsilon-subgradient descent methods for unconstrained nonsmooth convex minimization to constrained problems over polyhedral sets, in particular over Rp+. This is done by replacing the usual squared quadratic regularization term used in subgradient schemes by the logarithmic-quadratic distancelike function. We then obtain ?-subgradient descent methods, which allow us to provide a natural extension of bundle methods and Polyak's subgradient projection methods for nonsmooth convex minimization. Furthermore, similar extensions are considered for smooth constrained minimization to produce interior gradient descent methods.
|Date of Award||2007|
|Supervisor||Jean-Jacques STRODIOT (Supervisor), Van Hien NGUYEN (Jury) & Joseph WINKIN (Jury)|
Méthodes de points intérieurs du type gradient et ε-sous-gradient pour la minimisation avec contrainte convexe
Bonduel, L. (Author). 2007
Student thesis: Master types › Master in Mathematics